Cosmic-ray-produced Be-10 and Al-26 in riverborne quartz sediment are commonly used to estimate average watershed-scale erosion rates. Likewise, the concentrations of these nuclides in ancient sediments, stored in a depositional basin, carry a record of past erosion rates in the sediment source area. This is important because such a record could be compared to records of climate change or tectonic events to elucidate relationships between climate, tectonics, and erosion. If the sediments are shielded from the cosmic-ray flux after deposition, for example in deep water, their nuclide concentrations need only be corrected for radioactive decay since deposition in order to determine past erosion rates. Where sediment is deposited subaerially and buried relatively slowly, on the other hand, the additional nuclide concentration that builds up during sediment accumulation and storage must be reconstructed and subtracted in order to recover the initial nuclide concentrations in the sediment and thence the past erosion rates. We describe an example of this process for an early to middle Pleistocene section of alluvial sediment in Fisher Valley, Utah. We use stratigraphic observations as well as an independently known age model for the sediment section to: a) subtract postdepositional nuclide concentrations and reconstruct past erosion rates between 0.7-0.6 Ma, and b) estimate the uncertainty in the results that arises from imperfect dating of the section and the natural variability in accumulation rates. The present basin-averaged erosion rate in Fisher Valley is near 125 m/Myr, and middle Pleistocene basin-averaged erosion rates varied between 80-220 m/Myr. Changes in the erosion rate over time do not appear to be connected to glacial-interglacial climate changes, but may be related to episodic subsidence of the basin. Uncertainties are small in the case of low erosion rates and high sediment accumulation rates, and large in the opposite situation. In this example, we could reduce the uncertainties by increasing the sampling density or by better relating our sample locations to the small-scale stratigraphy of the sedimentary section. In general, future attempts to reconstruct past erosion rates from cosmogenic-nuclide concentrations in ancient alluvium will be most successful in situations where postdepositional nuclide accumulation is minimized, for example in lakes or marine basins.